Title:
|
Linearization by completely generalized input-output injection (English) |
Author:
|
López Morales, Virgilio |
Author:
|
Plestan, F. |
Author:
|
Glumineau, A. |
Language:
|
English |
Journal:
|
Kybernetika |
ISSN:
|
0023-5954 |
Volume:
|
35 |
Issue:
|
6 |
Year:
|
1999 |
Pages:
|
[793]-802 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
The problem addressed in this paper is the linearization of nonlinear systems by generalized input-output (I/O) injection. The I/O injection (called completely generalized I/O injection) depends on a finite number of time derivatives of input and output functions. The practical goal is the observer synthesis with linear error dynamics. The method is based on the I/O differential equation structure. Thus, the problem is solved as a realization one. A necessary and sufficient condition is proposed through a constructive algorithm and is based on the exterior differentiation. (English) |
Keyword:
|
linearization of nonlinear systems |
Keyword:
|
input-output injection |
Keyword:
|
exterior differentiation |
Keyword:
|
I or O differential equation structure |
Keyword:
|
observer synthesis |
MSC:
|
93B15 |
MSC:
|
93B18 |
MSC:
|
93C10 |
idZBL:
|
Zbl 1274.93061 |
idMR:
|
MR1747977 |
. |
Date available:
|
2009-09-24T19:30:11Z |
Last updated:
|
2015-03-27 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135326 |
. |
Reference:
|
[1] Bestle D., Zeitz M.: Canonical form observer design for nonlinear time varying systems.Internat. J. Control 38 (1983), 419–431 MR 0708425, 10.1080/00207178308933084 |
Reference:
|
[2] Birk J., Zeitz M.: Extended Luenberger observers for nonlinear multivariable systems.Internat. J. Control 47 (1988), 1823–1836 MR 0947071, 10.1080/00207178808906138 |
Reference:
|
[3] Chiasson J. N.: Nonlinear differential–geometric techniques for control of a series DC motor.IEEE Trans. Systems Technology 2 (1994), 35–42 10.1109/87.273108 |
Reference:
|
[4] Diop S., Grizzle J. W., Moraal P. E., Stefanopoulou A.: Interpolation and numerical differentiation for observer design.In: Proc. of American Control Conference 94, Evanston 1994, pp. 1329–1333 |
Reference:
|
[5] Fliess M.: Generalized controller canonical forms for linear and nonlinear dynamics.IEEE Trans. Automat. Control 35 (1990), 994–1001 Zbl 0724.93010, MR 1065035, 10.1109/9.58527 |
Reference:
|
[6] Glumineau A., Moog C. H., Plestan F.: New algebro–geometric conditions for the linearization by input–output injection.IEEE Trans. Automat. Control 41 (1996), 598–603 Zbl 0851.93018, MR 1385333, 10.1109/9.489283 |
Reference:
|
[7] Hammouri H., Gauthier J. P.: Bilinearization up to output injection.Systems Control Lett. 11 (1988), 139–149 Zbl 0648.93024, MR 0955483, 10.1016/0167-6911(88)90088-6 |
Reference:
|
[8] Keller H.: Nonlinear observer design by transformation into a generalized observer canonical form.Internat. J. Control 46 (1987), 1915–1930 Zbl 0634.93012, MR 0924264, 10.1080/00207178708934024 |
Reference:
|
[9] Krener A. J., Respondek W.: Nonlinear observers with linearizable error dynamics SIAM J.Control Optim. 23 (1985), 197–216 MR 0777456, 10.1137/0323016 |
Reference:
|
[10] López-M. V., Glumineau A.: Further results on linearization of nonlinear systems by input output injection.In: Proc. of 36th IEEE Conference on Decision and Control, San Diego 1997 |
Reference:
|
[11] Marino R.: Adaptive observers for single output nonlinear systems.IEEE Trans. Automat. Control 35 (1990), 1054–1058 Zbl 0729.93016, MR 1065044, 10.1109/9.58536 |
Reference:
|
[12] Marino R., Tomei P.: Dynamic output feedback linearization and global stabilization.Systems Control Lett. 17 (1991), 115–121 Zbl 0747.93069, MR 1120756, 10.1016/0167-6911(91)90036-E |
Reference:
|
[13] Phelps A. R.: On constructing nonlinear observers.SIAM J. Control Optim. 29 (1991), 516–534 Zbl 0738.93032, MR 1089143, 10.1137/0329030 |
Reference:
|
[14] Plestan F., Cherki B.: An observer for one flexible robot by an algebraic method.In: IFAC Workshop on New Trends in Design of Control Systems NTDCS’94, Smolenice 1994, pp. 41–46 |
Reference:
|
[15] Plestan F., Glumineau A.: Linearization by generalized input–output injection.Systems Control Lett. 31 (1997), 115–128 Zbl 0901.93013, MR 1461807, 10.1016/S0167-6911(97)00025-X |
Reference:
|
[16] Proychev T. Ph., Mishkov R. L.: Transformation of nonlinear systems in observer canonical form with reduced dependency on derivatives of the input.Automatica 29 (1993), 495–498 Zbl 0772.93017, MR 1211308, 10.1016/0005-1098(93)90145-J |
Reference:
|
[17] Williamson D.: Observation of bilinear systems with application to biological systems.Automatica 13 (1977), 243–254 10.1016/0005-1098(77)90051-6 |
Reference:
|
[18] Xia X. H., Gao W. B.: Nonlinear observers design by dynamic error linearization.SIAM J. Control Optim. 27 (1989), 1, 199–216 MR 0980230, 10.1137/0327011 |
. |